Related Experiment Video
Updated: Aug 12, 2025
07:42
Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
Published on: December 15, 2021
3.2K
Chimeras on a ring of oscillator populations
1School of Mathematical and Computational Sciences, Massey University, Private Bag 102-904, North Shore Mail Centre, Auckland, New Zealand.
Chaos (Woodbury, N.Y.)
|February 1, 2023
Summary
This study explores chimera states in coupled oscillator networks. Researchers found macroscopic chaos in networks with over five populations, suggesting it may disappear with more oscillators.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Network Science
Background:
- Chimera states exhibit coexisting synchronous and asynchronous oscillator groups in networks.
- Understanding chimera dynamics is crucial for complex system analysis.
Purpose of the Study:
- To analyze chimera states in ring networks of N populations.
- To derive and solve equations governing synchrony levels within each population.
- To investigate the emergence of macroscopic chaos in these networks.
Main Methods:
- Utilized the Ott/Antonsen ansatz to derive coupled ordinary differential equations.
- Employed a self-consistency argument to describe chimera states.
- Compared results for N=2, 3 with existing literature and extended to N=4-12.
Main Results:
- Derived ODEs for synchrony levels in N-population ring networks.
- Obtained new results for N=4-12 populations.
- Identified macroscopic chaos for N>5, with a conjecture on its vanishing for larger N.
Conclusions:
- The Ott/Antonsen ansatz provides a framework for studying chimera states.
- Macroscopic chaos is a feature of chimera states in networks with a moderate number of populations.
- Further investigation is needed to confirm the vanishing of chaos for very large N.
Related Concept Videos
02:52Resonance
54.7K
The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N-O and N=O bonds.
54.7K
01:06Forced Oscillations
6.6K
When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.
6.6K
02:33Stereoisomerism of Cyclic Compounds
9.1K
In this lesson, we delve into the role of ring conformation and its stability, which determines the spatial arrangement and, consequently, the molecular symmetry and stereoisomerism of cyclic compounds. 1,2-Dimethylcyclohexane is used as a case study to evaluate the possible number of stereoisomers. Here, given the multiple (n = 2) chiral centers, there are 2n = 4 possible configurations that lack a plane of symmetry, as the ring skeleton exists in a non-planar chair conformation. In addition,...
9.1K
01:30Oscillations In An LC Circuit
2.4K
An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by
2.4K
01:12Fermi Level Dynamics
308
The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
308
01:04Oscillations about an Equilibrium Position
5.5K
Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...
5.5K